Well, to join the medical corps, you have to have already completed medical school. If you're looking to join for help with tuition, the Navy, Army, and Air Force each have an HPSP program for that. The Navy additionally has HSCP, but it's not commonly used for medical school when compared to HPSP.
GMO stands for General Medical Officer. Pretty much, if you use HPSP and graduate, you will complete you first year of residency (PGY-1/intern year) to obtain a medical license. Before moving on to PGY-2, you then serve in a general medical role, being the primary care provider in various potential settings, then reapply to residency after the GMO tour to start PGY-2 (and in some cases PGY-1 again if procedure heavy/some surgical areas). For competitive specialties, GMOs are often done. GMOs are not limited to HPSP students or non-residency trained physicians to my current knowledge.
Are you maybe thinking of an enlistment? You state you're a pre-med which means you are working on pre-reqs most likely in undergrad, and I'm assuming you don't already have a degree, which means you're ineligible to become an officer (need at least a bachelors degree). That said.. enlisting will give you life experience for sure and earn you the Post-9/11 GI Bill assuming you serve 3 years on active duty, which can then pay for school (or most of it) without any additional obligation. But if your goal is to be in the medical corps, again, that will have to wait until after medical school.
However, I don't recommend joining in any capacity if your intention is solely, or mostly, based on having help with tuition/financial relief. Most people who do it for those reasons regret it. Those who serve because they want to serve often have a better experience.
You also have a large hurdle - that is getting into medical school. Worry about that before you worry about joining the medical corps for the obvious reasoning above, and/or speak to a recruiter about enlisting if that is what you meant.